The Wikipedia page for Arba'een Pilgrimage claims that "some Sunnis" make the pilgramage. It cites the following reference:
20 million Shia Muslims - as well as some Sunnis, Christians, Yazidi and other faiths - are on their way to Karbala, Iraq to participate in the world's largest annual gathering of people, the religious pilgrimage of Arbaeen. -- Mark Piggott, IBTimes.co.uk
It doesn't seem to be the most reliable reference; the comments indicate the author mistakenly wrote "Sunni pilgrimage of Hajj".
Question: Which Sunnis go on Arba'een Pilgrimage?